Shagari y la “economía mixta”

To validate the swept hybrid model designs, flow field and icing simulations were performed on each of the three models for selected conditions of Table IV. The flow fields were generated with Fluent, as described previously, and the ice shapes were then generated using LEWICE3D (TRAJMC3D version 2.47). Comparing the resulting ice shapes near the centerline of the IRT to those from the respective IFB case at the appropriate station allowed evaluation of the performance of the hybrid wing models in predicting the full-scale ice accretion.

Three test cases were selected for evaluating the models. Case WB33 T = –4 was selected because it had an attachment line location, airspeed, and angle of attack near the average of all the cases, making it a good candidate for general testing. Case WB71 T = –6 was selected for having the largest IFB aircraft angle of attack and an attachment line location that was farthest down the leading edge, requiring the most aggressive α and δ settings in the tunnel. The warmer temperatures for these two cases also produce glaze ice shapes with large upper horns that were sensitive to the local heat transfer coefficient, making it easier to determine when a good ice shape match was achieved. Case WB47 T = –6 was also used in this

research because the flight speed for this case exceeds the assumed IRT test section velocity limit of 250 kn (128.6 m/s). This provided an opportunity to investigate icing scaling methods in the case of the wind tunnel conditions being unable to match flight velocity. Results are shown for case WB 33 T = –4 for all three models; additional cases are shown only for the Midspan model to illustrate the comparison.

Table VII compares the conditions for the IRT simulations with those from the baseline analyses for the cases described above.

TABLE VII.—MIDSPAN MODEL FLOW FIELD AND ICING CONDITION COMPARISONS OF ICED FLIGHT BASELINE (IFB) WITH ICING RESEARCH TUNNEL (IRT) SIMULATIONS FOR THREE CASES

Condition Case

WB33 T = –4 WB47 T = –6 WB71 T = –6

IFB IRT IFB IRT IFB IRT

Static pressure, Pamb, kPa 69.702 90.011 57.209 88.658 95.956 91.882

Air density, ρ, kg/m³ 0.9027 1.1653 0.7464 1.1563 1.2519 1.1984

Reynolds number based on

model chord, Rec, ×10⁶ 28.9 16.0 28.1 17.2 35.2 14.5

Airspeed, V, m/s 119.41 119.41 139.6 128.61 104.51 104.51

Static temperature, Tamb, °C –4 –4 –6 –6 –6 –6

Mach number (M) 0.363 0.363 0.426 0.393 0.319 0.319

Liquid water content, g/m³ 0.551 0.551 0.509 0.467 0.509 0.509

Median volumetric diameter, μm 20 20 20 20.88 20 20

Droplet distribution Langmuir D 10-bin IRT Langmuir D 10-bin IRT Langmuir D 10-bin IRT

Icing time, min 45 45 45 53.3 15 15

Angle of attack, α, deg 3.67 3.67 4.36 4.36 4.4 4.4

Flap angle, δ, deg NA 15 NA 16 NA 15

While the LEWICE3D simulations for the IFB were performed at pressure altitude listed on Table IV and utilized a Langmuir D (Ref. 23) droplet size distribution consistent with that found in flight

conditions, the hybrid wing models were simulated utilizing the IRT pressure and the 10-bin IRT droplet size distribution based on the values measured experimentally inside the IRT by Papadakis et al. (Ref. 43) in 2004,¹ with the exception of the Inboard hybrid wing model, which had to be simulated utilizing a monodisperse droplet size distribution due to memory limitations of the Taub supercomputer cluster at the University of Illinois. The differences between the CFB/IFB simulations and those done in the IRT are detailed in Table VII.

Figure 33, Figure 34, and Figure 35 show comparisons in ice shape and collection efficiency between the LEWICE3D simulations of the IFB and the three models in the IRT for case WB33 T = –4. The ice shapes for the IRT hybrid wing models are shown in 3D view for Figure 33(a) for the Inboard model, Figure 34(a) for the Midspan model, and Figure 35(a) for the Outboard model, where the squares indicate the stagnation point location for the respective cuts near the centerline of the tunnel. The same three ice shapes near the centerline of the tunnel are also displayed in 2D view in comparison with the

corresponding IFB ice shape in Figure 33(b), Figure 34(b), and Figure 35(b) for the Inboard, Midspan, and Outboard models, respectively. Overall, good agreement was observed in the ice shape comparison, meaning horn lengths were within about 20 percent and horn angles were within the variation of the three cuts near the centerline (±6 in.). Local collection efficiencies between the IFB and IRT simulations are displayed in Figure 33(c), Figure 34(c), and Figure 35(c) for the Inboard, Midspan, and Outboard models, respectively, in which location and magnitude of the collection efficiency peak were in good agreement, with the exception of the Inboard model, which presented the poorest agreement among the three models.

This could be attributed to a few different factors, including the lack of a satisfactorily converged CFD 3D RANS solution for the Inboard model, the inability to simulate the model with a 10-bin IRT droplet distribution in LEWICE3D, and higher pressure and density at the IRT that led to higher heat transfer coefficients and larger horn lengths.

Figure 36, Figure 37, and Figure 38 show the centerline ice shapes on the Midspan model for the three cases detailed in Table VII as well as the ice shapes at 6 in. above and below the centerline. The effect of the spanwise variation in the attachment line on the ice shape can be seen in Figure 33 to Figure 38. These variations were no larger than the variation between the centerline ice shape from the IRT simulations and the IFB. Generally, the agreement between ice shapes from the IFB and the hybrid models is quite good.

1Although it was later determined that the 10-bin IRT droplet size distribution is not really representative of the actual IRT spray system, it was deemed appropriate for the model-design simulations.

Figure 33.—Inboard model LEWICE3D simulations, case WB33 T = –4 where angle of attack α is 3.67° and flap angle δ is 6°. (a) IRT (Icing Research Tunnel) ice shapes.

(b) IRT ice shape compared with iced flight baseline (IFB).

(c) IRT collection efficiency compared with IFB.

Figure 34.—Midspan model LEWICE3D simulations, case WB33 T = –4 where angle of attack α is 3.67° and flap angle δ is 15°. (a) IRT (Icing Research Tunnel) ice shapes.

(b) IRT ice shape compared with iced flight baseline (IFB).

(c) IRT collection efficiency compared with IFB.

Figure 35.—Outboard model LEWICE3D simulations, case WB33 T = –4 where angle of attack α is 3.67° and flap angle δ is 11°. (a) IRT (Icing Research Tunnel) ice shapes.

(b) IRT ice shape compared with iced flight baseline (IFB).

(c) IRT collection efficiency compared with IFB.

The discrepancies seen in Figure 36, Figure 37, and Figure 38 between the hybrid model ice

accretions and those from the IFB can be attributed to a few different factors. First, the simulations done for the hybrid models were performed at IRT pressure, while the IFB simulations were done at pressure altitude. Other factors also play a role in causing the different ice accretions. To explain some of the discrepancies between the hybrid models and the IFB, the local collection efficiency and heat transfer coefficient for case WB33 T = –4 are presented in Figure 39 for simulations done for the hybrid models utilizing both the local IRT pressure and the pressure altitude of the IFB.

Figure 36.—Midspan model ice shapes for case WB33 T = –4 where angle of attack α is 3.67° and flap angle δ is 15° at Icing Research Tunnel (IRT) pressures and iced flight baseline (IFB) at pressure altitude.

Figure 37.—Midspan model ice shapes for case WB47 T = –6 where angle of attack α is 4.36° and flap angle δ is 16° at Icing Research Tunnel (IRT) pressures and iced flight baseline (IFB) at pressure altitude.

Figure 38.—Midspan model ice shapes for case WB71 T = –6 where angle of attack α is 4.40° and flap angle δ is 15° at Icing Research Tunnel (IRT) pressures and iced flight baseline (IFB) at pressure altitude.

Figure 39.—Midspan model comparison of (a) local collection efficiency β and (b) convective heat transfer coefficient hc for case WB33 T = –4 in Icing Research Tunnel (IRT) at IRT (local) and iced flight baseline (IFB) (altitude) pressures.

When running the LEWICE3D simulation of the IRT model at the same pressure as the flight

condition (IFB), the local collection efficiency peak, β^max, on the IRT model is somewhat higher than that of the IFB, whereas the heat transfer coefficient, hc, is well matched. This results in a larger horn due to the extra impinging mass of water in the horn area of the model upper surface. The β^max value is likely larger due to the lower maximum thickness of the hybrid model as compared with the baseline airfoil. For a hybrid model, geometry similitude is achieved by retaining the full-scale geometry at the leading edge, but the full-scale geometry can only be maintained over a small portion of the airfoil, up to the leading-edge extents. The leading-leading-edge extents are generally selected based on the expected impingement limits.

Beyond these points the leading edge is blended with the redesigned aft section of the model. Because the leading-edge extents rarely extend to the point of maximum thickness on the airfoil, this usually results in a hybrid model with a lower maximum thickness than the reference airfoil. The differences between the thickness of the hybrid and the thickness of the full-scale airfoil are shown in Table V. For the Inboard model, the difference in total thickness is significant, resulting in loss of about half of the total full-scale thickness. Streamlines and droplet trajectories upstream of a thick geometry are influenced more than for a thinner body. Thus, icing cloud droplets impinge on the leading edge of the airfoil at a lesser rate for thicker airfoils in comparison with thinner ones. For this reason, hybrid models often result in higher β^max than the reference geometry for the same conditions because the hybrid is substantially thinner than the reference geometry it represents. Such a trend of higher β^max for the hybrid models compared with the corresponding full-scale stations was seen in the icing simulation results for cases WB33 T = –4, WB47 T = –6, and WB71 T = –6 (see Figure 36, Figure 37, and Figure 38).

Additionally, when the IRT model is simulated at the local atmospheric pressure, the effects are reversed with a well-matched β distribution but considerably higher h^c. This also leads to a larger horn on the IRT model than the IFB because more of the water that impinges near the horn region is frozen due to the higher heat transfer. The increase in magnitude of the heat transfer is caused by the higher density of the air at the IRT and is the most apparent effect of altitude. Thus, attempting to match either the IFB β by simulating the IRT model at the IFB pressure or to match the IFB hc by simulating the IRT model at the local elevation pressure yields similar ice accretions that both have longer horns than the IFB.

The ice shapes for the Outboard and Inboard models at their design angle of attack and flap deflection were shown in Figure 35 and Figure 33. The ice shape on the Outboard model matches the IFB well at the centerline of the IRT. As discussed previously, the Inboard model ice shapes have a longer horn length compared with the IFB due to the difference in total thickness of the model compared with the full-scale baseline.

Figure 40.—Effect of attachment line location on centerline ice shape of Midspan model compared with iced flight baseline (IFB) (condition WB33 T = –4). (a) Different flap angles δ where angle of attack α = 3.67°. (b) Different angles of attack α where flap angle δ = 5.0°.

The effect of the position of the attachment line is illustrated in Figure 40 for the Midspan model. For the same input flow conditions, the changing angle of attack or flap deflection angle changes the location of the attachment line at the centerline of the IRT. As discussed previously in the 2D analysis, the attachment line location has a first-order effect on the ice shape that forms on the airfoil or wing. Either method for changing the attachment line location (changing the geometric angle of the model or moving the flap) can be used. Figure 40 illustrates the ice shape variations that result from changing the

attachment line location.

The appendixes include additional LEWICE3D calculations for studies that investigated spanwise ice shape variation due to changes in attachment line location, the necessity of setting the proper geometric angle of attack compared with simply setting the desired attachment line location, and formation of ice shapes for stations along the baseline model for locations other than the three for which models are being constructed.